Factor 3x^2+11x-20

Problem

3*x2+11*x−20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=11 and c=−20

2. Find two numbers that multiply to a⋅c=3⋅(−20)=−60 and add to b=11

3. Determine the factors of −60 that satisfy the condition: the numbers are 15 and −4 since 15⋅(−4)=−60 and 15 + (-4) = 11$.

4. Rewrite the middle term 11*x using the two numbers found: 15*x−4*x

3*x2+15*x−4*x−20

5. Factor by grouping the first two terms and the last two terms.

3*x*(x+5)−4*(x+5)

6. Factor out the common binomial (x+5)

(3*x−4)*(x+5)

Final Answer

3*x2+11*x−20=(3*x−4)*(x+5)

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